Why is a hazelnut called a Noisette in France?
"Noisette sometimes called "filbert" is the fruit of the common hazel ( Corylus avellana ), and various species of the genus Corylus . By metonymy , the term also refers to the seed (or almond) contained in this fruit that is edible." [3]

Noisette is a diminutive for Noix (nut) One French site the reason Noisette is the more common name may be because in some varieties of Aveline's the husk fully opens to release the Noix hence the name Noisette.

Aveline as a name:
"Aveline is the French femenine form corresponding to the Spanish Avelino/Avelina, the Italian Avellino/Avellina and the Catalan Avel·lí/Avel·lina. These names come from the Roman Latin proper name Avellinus/Avellina, a Campanian cognomen derivated from the demonym avellinus, avellina, "from Avella/Abella", capital of the Roman province of the Campania.

The old and dialectal (basically southern) French word aveline (hazelnut), same that the Occitan avelana and the Spanish and Catalan avellana, comes from the Latin nux avellana or nux abellana, "nut from Avella/Abella", because Avella was the center of production and commercialisation of hazelnuts." [4]

Avella is in the province of Avellino, part of the Compania region that was conquered by the Normans in the 11th century.

From wikipedia's entry on the city of Avella: "Virgil and Silius Italicus considered that its territory was not fertile in corn, but rich in fruit-trees (maliferae Abellae): the neighborhood also abounded in filberts or hazelnuts of a very choice quality, which were called from thence nuces Avellanae." [5]

2) Is the word Aveline related to Avis, the latin word bird?
I dont think so since basically the Normans brought it over with them and Avella doesnt seem connected to Avis but I cant be completely sure since I dont know much about latin.

Etymology on Avis[7] I didnt think it was connected to Evelyne/Evelyn either but amberdaydream pointed out Evelyn stems from Aveline. Again I dont know much about that.

So name enthusiasts and etymologists what do you think about the name? Do you have any information or corrections??? I think it makes a very interesting and sweet name!

Here are my sources, sorry most of them are not in English. I am really bad at citing things so Im not sure these are all in the right order.

Brilliant job piling up all the research! Aveline is a relatively obscure name so it's astonishing that it has all this history, IMO!

I'm uncertain that Aveline is related to Avis as well, since it's debated whether Avis is directly from avis meaning "bird" or whether it's simply associated with it for having the same spelling. Apparently Avis as a given name is from the name Aveza*, which would likely separate Avis from Aveline.
*http://www.behindthename.com/name/aveza - the owner of the site has left a source of their own for this info.

@amberdaydream: thanks so much for providing some of it and for the interesting debate! Honestly I have looked at the word hazelnut and Aveline for so long recently that my head is spinning lol but hopefully all of this is accurate.

@amber here is some more interesting info that is better worded then what I post

The hazel is a bush or a small tree, of the family betulaceae and the genus corylus, and the European species is the Corylus avellana.

In Modern French hazel is le noisetier, a form which dates from 1530, and is derived from the word for the nut, noisette. The Latin name shows the source of two early regional variants from the thirteenth century: avelinier and coudrier.

Avelinier

Aveline is a shortened form of nux abellana, from Abella, a town in Campagna, Italy, where the nuts were extensively cultivated. Here, the nut is usually taken to be the elongated form, more almond in shape. Avelinier is the tree.

In English, this cultivated variety is sometimes known as the filbert, which is probably short for the filbert nut, that is the nut of SaintPhilbert, since it is said to be ripe on his feast day, 22nd September.

From aveline comes Aulanède in Provence, which signifies a place where there was a plantation of hazel trees. Orignolles, in Charente-Maritime, is from the same root...

The hazelnut also has heraldic connections.

They include, rarely, the croix avellane, which is formed by four hazelnuts joined in cross, and the coquerelle, three hazelnuts in the form of a letter T. This last derives from French coque, shell.